LaTeX Math Equations - Posts

Having math equations in a report can be painful. Here are some LaTeX commands often used in scientific reports. I will try to keep this post updated.

The LaTeX rendering on this website is done by an open-source package KaTeX.

Full list of supported symbols of Katex: Supported Functions
Also check https://www.mathcha.io/editor for a powerful online math and diagram editor.

Common Structures

LaTeX Code	Output
`\frac{abc}{xyz}`	$\frac{abc}{xyz}$
`\overline{abc}`	$\overline{abc}$
`\underline{abc}`	$\underline{abc}$
`\overrightarrow{abc}`	$\overrightarrow{abc}$
`\overleftarrow{abc}`	$\overleftarrow{abc}$
`\sqrt{abc}`	$\sqrt{abc}$
`\sqrt[n]{abc}`	$\sqrt[n]{abc}$
`\widehat{abc}`	$\widehat{abc}$
`\widetilde{abc}`	$\widetilde{abc}$
`𝚏''`	$f''$
`\overbrace{abc}`	$\overbrace{abc}$
`\underbrace{abc}`	$\underbrace{abc}$
`\underbrace{x+\cdots+x}_{n\text{ times}}`	$\underbrace{x+\cdots+x}_{n\text{ times}}$
`\frac{\partial y}{\partial x1}`	$\frac{\partial y}{\partial x1}$
`\frac{\mathrm{d} Q}{\mathrm{d} t}`	$\frac{\mathrm{d} Q}{\mathrm{d} t}$
`\sum^{n}_{i=1}`	$\sum^{n}_{i=1}$
`\prod^{n}_{i=1}`	$\prod^{n}_{i=1}$
`\lim_{x\to\infty} f(x)`	$\lim_{x\to\infty} f(x)$
`\int_{a}^{b} x^2 dx`	$\int_{a}^{b} x^2 dx$

Math Operators

Code	Output
`\delta`	$\delta$
`\Delta`	$\Delta$
`\nabla`	$\nabla$
`\forall`	$\forall$
`\mathbb{R}`	$\mathbb{R}$
`\in`	$\in$

Arrows and Brackets

Code	Output
`\leftarrow`	$\leftarrow$
`\Leftarrow`	$\Leftarrow$
`\rightarrow`	$\rightarrow$
`\Rightarrow`	$\Rightarrow$
`\leftrightarrow`	$\leftrightarrow$
`\Leftrightarrow`	$\Leftrightarrow$

Greek Letters

\alpha α \beta β \gamma γ \delta δ \epsilon ϵ \zeta ζ \eta η \theta θ \iota ι \kappa κ \lambda λ \mu μ \nu ν \xi ξ \omicron ο \pi π \rho ρ \sigma σ \tau τ \upsilon υ \phi ϕ \chi χ \psi ψ \omega ω \varepsilon ε \vartheta ϑ \varkappa ϰ \varpi ϖ \varrho ϱ \varsigma ς \varphi φ \digamma ϝ

Sample Equations

1. Code

rac{mathrm{d}}{mathrm{d} x}left[|w x-y|^{2}\right]=2(w x-y) cdot w

1. Output

\frac{\mathrm{d}}{\mathrm{d} x}\left[|w x-y|^{2}\right]=2(w x-y) \cdot w

2. code

sigma=rac{e^z}{1+e^z}

sigma’=rac{e^z}{(1+e^z)^2}=rac{e^z}{1+e^z} cdot rac{1}{1+e^z} =sigma(1-sigma)

2. Output

(\underbrace added)

\sigma = \frac{e^z}{1+e^z}

\sigma^{\prime}=\frac{e^{z}}{\left(1+e^{z}\right)^{2}}=\underbrace{\frac{e^{z}}{1+e^{z}}}_{\sigma} \cdot \underbrace{\frac{1}{1+e^{z}}}_{1-\sigma}=\sigma(1-\sigma)

3. Code

left{
             egin{array}{lr}
             x=dfrac{3pi}{2}(1+2t)cos(dfrac{3pi}{2}(1+2t)), &  \
             y=s, & 0leq sleq L,|t|leq1.\
             z=dfrac{3pi}{2}(1+2t)sin(dfrac{3pi}{2}(1+2t)), &
             end{array}
\right.

3. Output

\left\{ \begin{array}{lr} x=\dfrac{3\pi}{2}(1+2t)\cos(\dfrac{3\pi}{2}(1+2t)), & \\ y=s, & 0\leq s\leq L,|t|\leq1.\\ z=\dfrac{3\pi}{2}(1+2t)\sin(\dfrac{3\pi}{2}(1+2t)), & \end{array} \right.